Adaptive Kalman filter based on variance component estimation for the prediction of ionospheric delay in aiding the cycle slip repair of GNSS triple-frequency signals

In order to incorporate the time smoothness of ionospheric delay to aid the cycle slip detection, an adaptive kalman filter is developed based on variance component estimation. the correlations between measurements at neighboring epochs are fully considered in developing a filtering algorithm for colored measurement noise. within this filtering framework, epoch-differenced ionospheric delays are predicted. using this prediction, the potential cycle slips are repaired for triple-frequency signals of global navigation satellite systems. cycle slips are repaired in a stepwise manner; i.e., for two extra wide lane combinations firstly and then for the third frequency. in the estimation for the third frequency, a stochastic model is followed in which the correlations between the ionospheric delay prediction errors and the errors in the epoch-differenced phase measurements are considered. the implementing details of the proposed method are tabulated. a real beidou navigation satellite system data set is used to check the performance of the proposed method. most cycle slips, no matter trivial or nontrivial, can be estimated in float values with satisfactorily high accuracy and their integer values can hence be correctly obtained by simple rounding. to be more specific, all manually introduced nontrivial cycle slips are correctly repaired.